?How to fine tune operation of postwar Lionel NW Switcher?

If you haven't already, pull the motor from the truck and check the thrust of the motor shaft. Also make sure the worm gear on the axle has minimal side to side play and is centered. Some shimming may be required.

Pete

Check for continuity between the 3 segments on the armature.  All three must have continuity with each other.  If not, theres an "open" / broken wire on one of the coils underneath.  Most likely where it is soldered to the segment.  JMHO  

bob

Is it a Lionel Seaboard #602 by any chance?

I have had pretty good luck restaking the fields on these locos, if you look at a copy of the Lionel repair manual, it will show how and where. A sharp chisel works best to spread the staking. Also the other items mentioned are good to check also. Clean the brushes, brush holders, and install new brush springs on the brush caps. As for the horn, make double sure you have a new battery, and use some extra fine sand paper to clean the contact areas of the relay. Give it a sprits of electrical cleaner and blow dry with canned air. You can try giving it a jolt of low voltage electricity from a transformer, six volts is more than enough. Sometimes a tap on the horn while applying voltage will help the contacts clean themselves. New horns are available and are moderately priced. Let us know how you make out. 

 Tapping on the horn may get it working. If it does make noise, play it long and turn it so debris can fall out. Some horns have a screw & locknut adjustment for tone and volume. Loosening(OK) and tightening ( slightly ) may loosen the diaphragm if stuck. So might oil inside it.

Don't get carried away with tightening the staking on those motors. It is fairly easy to distort the motor truck and make the binding worse.
As Rob wrote, the problem can usually be traced to the black plastic cover at the bottom of the motor becoming loose.
That cover acts as the lower armature bearing.
You can move it from side to side while the motor is running, and feel it slow down and speed up.

I used to use paper match sticks with the head cut off to shim the plate to the good position.

Re: horn

If tapping does not work, the brief application of about 12 volts AC may get it going.
Sometimes you need to do both (12 volts and a sharp tap).

When I tap, I use the handle of a small screw driver to tap the diaphragm through the hole in the face of the horn. I don't think I've ever tried tapping on the case.

Quite simply, use a PW transformer or something like an MPC pure power transformer. The sharktooth output of modern transformers doesn't play nice with the old motors.

I also think that the DC offset of the Z-4000 is not sufficient to activate the horn.

I may be wrong...

I also think that the DC offset of the Z-4000 is not sufficient to activate the horn.

If that was the case, the relay would not activate. In his first post, CTR says the relay works.

Another potential problem: the battery holder may need cleaning to improve conductivity. He can try bypassing everything by connecting leads from a known good battery to the horn. I use an inexpensive Radio Shack battery holder to keep a test battery handy. One lead to a clean spot on the case, the other lead to the terminal where the horn is connected to the relay.